Automotive crash testing is very expensive to carry out in terms of time and money. In this day and age, it is simply not practical to use a methodology of making an engineering estimate, mocking up a sample, testing, then modifying and retesting. Program timing and budgets would typically allow for one round of vehicle crash testing as a final validation. This being the case, simulation has found wide application in the development phase. With this, a virtual model is built, typically with commercially available codes and crash conditions simulated. The configuration can then be modified and optimized before physical prototypes are made.
One application of automotive crash simulation is in the development of fuel delivery modules. With reference to FIG. 1, a fuel delivery module (FDM), generally indicated at 11, is a device mounted into the fuel tank (not shown) of a vehicle which draws fuel up and delivers it to the engine at a predefined pressure. The portion of the FDM which engages the top of the fuel tank is a flange 10 made, in most cases, of plastic. This flange is sealed to the tank by an O-ring and held in place by a steel lock ring. The flange 10 is supported by struts 14 above a fuel pump 12 that is typically disposed in a reservoir (not shown). Hoses (not shown) are used to fluidly couple the fuel pump 12 to the flange 10 so that fuel may be delivered from the fuel pump through the flange.
There are several performance requirements of the FDM. One of these requirements, FMVSS 301, spells out specific crash tests and sets forth tolerable amounts of fuel which may spill. To meet this requirement, the FDM flange must not be breached. Internal damage is allowed, provided it does not allow fuel spillage. Another requirement of a specific FDM which is customer driven is that the FDM must remain fully functional, without damage, after a 10 mph vehicular impact. For the customer, 10 mph corresponds to the point at which the air bag is deployed. It is desired that if the air bag is not deployed due to a lower speed impact, the only damage to the vehicle would be visible to the outside, such as bumpers or panels. Requirements such as these have a major effect on what the FDM configuration will be.
To meet impact requirements, design engineers rely heavily on simulation to help point out strengths or weaknesses in their designs. Even though an engineer may have years of experience, it is difficult to predict what might happen in all instances without the use of simulation. This is due in part because the basic configuration is evolving. The concept of delivering fuel to the engine is mature. But, how this is done has been changing. Pressure regulation and filtering has been included with the fuel pump as a modular unit. This has resulted in cost savings and ease of assembly and servicing. Additionally, plastics are becoming favored over steel because of cost and weight savings. This all adds complexity that the engineer must consider when designing to meet crash requirements making simulation an even more important and useful tool.
Simulation of structural transients by FEA involves solving a second order equation:[M]{a}+[C]{v}+[K]{u}={F}
Where:                [M]=structural mass matrix        [C]=structural damping matrix        [K]=structural stiffness matrix        {a}=nodal acceleration vector        {v}=nodal velocity vector        {u}=nodal displacement vector        {F}=applied load vector        
Two methods of solving this equation include implicit time integration and explicit time integration. Both methods proceed through time in finite steps. The two methods are somewhat different in how they are performed and where they can be applied to obtain a solution in the most efficient manner.
Because the embodiment proposes use of the explicit method, details of the implicit method will not be discussed. However, several characteristics, advantages and disadvantages are given for comparison. The implicit method solves for displacements {u} first and then calculates the remaining quantities. As such, inversion of the stiffness matrix [K] is required. This step is computationally expensive. If the simulation is non-linear, [K] will be a function of {u} and an iterative technique such as Newton-Raphson is typically used. This can require many inversions of [K], greatly increasing the computational cost. An advantage of the implicit method is the fact that it is stable for large time steps. An excellent example of an application where this would be useful is in creep calculations.
The explicit method, like the Central Difference Method used in LS-DYNA (a finite element program of Livermore Software Technology Corp.), solves for accelerations first. Then other quantities are calculated. To do this, an internal force vector is created consisting of inertial forces [M]{a}, damping forces [C]{v}, and elastic forces [K]{u}. The internal force vector is combined with the external applied load vector and accelerations found using Newton's Second Law, F=Ma. Inversion of the mass matrix is required for solution. However, because the lumped mass approximation is used, the mass matrix is diagonal and inversion is trivial. The process is repeated as the solution is stepped through time. For stability, there is a maximum time step related to the speed of sound through the smallest element. This time step is usually quite small. For computational efficiency, a very regular mesh is desired. There is also a technique called mass scaling. This increases the density of the smallest elements in an attempt to achieve a larger time step. If there are very few small elements, a large increase in time step can be realized with a very small increase in mass. This can help keep required computer resources reasonable.
A major advantage of the explicit method is in the handling of non-linearities. Regardless of the non-linearites present, an internal force vector is created and accelerations are calculated effectively by matrix multiplication. The computational cost remains about the same. If the implicit method were used, non-linearities would typically be accounted for in the stiffness matrix. As it becomes more highly non-linear, many inversions may be required in an iterative process for convergence greatly increasing the computational cost.
Typical uses of the explicit method include short duration transient simulations and highly non-linear events, such as crash and impact analysis, simulating explosive events such as air bag deployment, etc.
The explicit method in LS-DYNA is currently used to evaluate fuel delivery modules under impact loadings. A conventional module mesh for a fuel delivery module 11 is shown in FIG. 2. There are two primary requirements that need to be met. First, the plastic flange 10 must not be breached under impact loading as per 49 CFR 571.301 (FMVSS 301). This behavior is considered to be of utmost importance for the vehicle safety: In case of a severe vehicle crash, everything inside the fuel tank is allowed to be rendered non-functional. However the tank vessel as a whole must remain sealed. Otherwise, fuel would be allowed to leave the tank causing a hazardous situation. To accomplish this sealing property, the module is configured in such a way as to separate in a prescribed location away from the upper surface. In FIG. 2, a strut boss 16 has a geometric stress raiser in that it is squared off and stepped in the location where separation is intended. Additionally, the strut rod 14 is press fit into the boss 16 almost to the step. The interference creates strain in the polymer adding pre-load to the intended separation area.
The second requirement to be met is that the module must be fully functional after a prescribed low speed impact. This means the strut boss 16 must not separate upon low speed impact and the strut rods must not take a permanent set from bending, among other things. It is noted that if the strut rod 14 is constructed with a stiffer geometry (thicker wall), or is made of a higher yielding steel, permanent deformation will be less likely, but more energy will be transferred to the strut boss 16 increasing the chance of separation.
As shown in FIG. 2, the conventional FEA model is constructed with a hexahedral mesh in the areas of concern which include the area off the strut boss 16, the flange 10 and strut rods 14. The bottom unit (including reservoir 18 and pump 12 therein) is constructed of shell elements and is treated as rigid. This means the displacements at each of the nodes are tied so there are only six degrees of freedom for the lower unit. This slims down the computational requirements. Spring elements 22 simulate the springs around the strut rods 14. The fuel tank environment 20 is constructed with a coarse shell mesh. The flange 10 of the module is tied to the tank environment 20. Loads can be applied to the tank environment from a previously run global analysis or can simply be prescribed. Contact within the model is penalty based meaning the following: as an element defined as contact passes through an element defined as target, a force is created which has a magnitude of element stiffness, multiplied by area, multiplied by the penetration distance, multiplied by a penalty value. The direction of the force is such that the contact element is pushed back away from the target element, preventing penetration as a consequence.
Several material models are used within the conventional simulation. For the polymer, an isotropic hardening plasticity model is used. This model works well with geometric non-linearities such as large deflection, but since the Bauschinger effect is not included, is not as useful for cyclic loading. The steel strut rod uses an elastic material model and the bottom unit uses a rigid material model. Stiffness is still assigned to the rigid model even though the model doesn't deform. This is so the contact forces can be correctly assessed.
The conventional simulation correctly predicts where strain buildup will occur in the polymer flange and therefore where fracture would be expected. However, separation takes place as the strut rod slides out of its press fit. In testing, separation occurs as a fracture. Also, at what impact magnitude separation occurs is not well predicted. Additionally, permanent deformation of the strut rod is not predicted because an elastic material model is currently in use.
Thus, there is a need to provide a simulation for a fuel delivery module that will correctly address the above deficiencies of the conventional simulation.